What is the axis ((x+4)^2)/9+((y-6)^2)/(25)=1 ?

The axis ((x+4)^2)/9+((y-6)^2)/(25)=1 is semi-major axis b=5, semi-minor axis a=3

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axis ((x+4)^2)/9+((y-6)^2)/(25)=1

axis

\frac{( x + 4 ) ^{2}}{9} + \frac{( y - 6 ) ^{2}}{25} = 1

semi - major axis b = 5, semi - minor axis a = 3

Solution steps

\frac{( x + 4 ) ^{2}}{9} + \frac{( y - 6 ) ^{2}}{25} = 1

Rewrite

\frac{( x + 4 ) ^{2}}{9} + \frac{( y - 6 ) ^{2}}{25} = 1

in the form of the standard ellipse equation

\frac{( x - ( - 4 ) ) ^{2}}{3 ^{2}} + \frac{( y - 6 ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 4, 6), a = 3, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 4, 6), b = 5, a = 3

6.25 x^{2} + 16 y^{2} - 12.5 x + 64 y - 29.75 = 0

4 x^{2} + 49 y^{2} = 196

\frac{( x - 1 ) ^{2}}{25} + \frac{( y + 3 ) ^{2}}{16} = 1

3 x^{2} + y^{2} - 24 x + 39 = 0

\frac{x ^{2}}{5} + \frac{y ^{2}}{9} = 1

What is the axis ((x+4)^2)/9+((y-6)^2)/(25)=1 ?
The axis ((x+4)^2)/9+((y-6)^2)/(25)=1 is semi-major axis b=5, semi-minor axis a=3